In cryptography, secret sharing refers to any method for distributing a secret among a group of participants, each of which is allocated one or more shares of the secret. The secret can only be reconstructed when a required number of shares are combined together; individual shares are of no use on their own.
A secure secret sharing scheme distributes shares so that anyone with fewer than the required shares has no extra information about the secret than someone with zero shares. Some secret sharing schemes allow the secret to be reconstructed by a subset of the total number of generated shares. Thus, a secret can be reconstructed even when some of the shares are lost or when some of the shareholders are absent. In general, secret sharing schemes are based on mathematical problems that are “easy” to solve with a threshold amount of information, but “hard” without that threshold amount.
Conventional secret sharing schemes are based on polynomial interpolation, linear equation interpolation, simultaneous systems of linear equations, and simultaneous systems of modular equivalences. These secret sharing schemes have different degrees of complexity and different requirements. The amount of information held by each shareholder also varies from one scheme to another.